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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 27 Nov 2017 21:59:32 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Nov/27/t15118164411vrfzzwnjyxmqx8.htm/, Retrieved Sat, 18 May 2024 16:42:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308251, Retrieved Sat, 18 May 2024 16:42:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact134
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2017-11-27 20:59:32] [ee3b8eefe40cbbf7582280be5ca2feb3] [Current]
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Dataseries X:
1028
869
2698
2367
1928
1846
1404
1316
1008
865
586
343
1143
1807
2380
2334
2116
1788
1571
1306
952
806
473
278
993
1038
2259
2283
1746
1515
1230
882
1028
704
390
238
594
692
2125
1849
1468
1531
1203
878
818
605
316
136
528
654
1892
1597
1515
1241
1026
758
733
481
280
117
651
611
1898
1385
1047
1007
842
827
711
443
313
202
473
566
1609
1296
1153
1155
859
798
557
402
223
153
548
647
1757
1326
1308
1175
992
808
758
551
310
146
649
602
1801
1481
1400
1319
1153
950
829
636
310
191
679
842
1975
1677
1418
1540
1173
941
989
614
352
405




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308251&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=308251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308251&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0217668136207763
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0217668136207763 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308251&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0217668136207763[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308251&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0217668136207763
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326987101988
423672582.2724254781-215.272425478103
519282246.58663071503-318.586630715029
618461800.6520149021845.347985097816
714041719.63909604189-315.639096041886
813161270.7686386669145.2313613330882
910081183.75318127886-175.753181278863
10865871.927594538708-6.92759453870758
11586728.776802879543-142.776802879543
12343446.669006821894-103.669006821894
131143201.412462872151941.587537127849
1418071021.90782330046785.092176699542
1523801702.99677838581677.003221614193
1623342290.7329813313543.2670186686519
1721162245.67476646264-129.674766462635
1817882024.85215998973-236.852159989726
1915711691.69664316755-120.696643167551
2013061472.06946183107-166.069461831069
219521203.45465880729-251.45465880729
22806843.981292114956-37.9812921149559
23473697.154560408413-224.154560408413
24278359.275429869756-81.2754298697564
25993162.506322735833830.493677264167
261038895.583523822075142.416476177925
272259943.6834767155681315.31652328443
2822832193.3137263302389.6862736697726
2917462219.26591073354-473.265910733539
3015151671.96441986154-156.964419861536
3112301437.54780458932-207.547804589316
328821148.03015020942-266.030150209419
331028794.239521512304233.760478487696
34704945.327742279449-241.327742279449
35390616.074806291729-226.074806291729
36238297.153878118824-59.1538781188242
37594143.866286678866450.133713321134
38692509.664263321155182.335736678845
392125611.633131317851513.36686868215
4018492077.57430588831-228.574305888312
4114681796.59897157354-328.598971573543
4215311408.44641900332122.553580996677
4312031474.11401995944-271.114019959437
448781140.212731617-262.212731617
45818809.5051959588988.49480404110193
46605749.690100775206-144.690100775206
47316533.540658318861-217.540658318861
48136239.805491354293-103.805491354293
4952857.5459765711709470.454023428829
50654459.786261616291194.213738383709
511892590.0136758622831301.98632413772
5215971856.35376951659-259.353769516588
5315151555.70846435368-40.708464353675
5412411472.8223707973-231.8223707973
5510261193.77633645903-167.776336459029
56758975.124380213349-217.124380213349
57733702.39827429671830.6017257032817
58481678.064376356576-197.064376356576
59280421.774912805128-141.774912805128
60117217.688924701997-100.688924701997
6165152.4972476443319598.502752355668
62611599.52474550637911.4752544936206
631898559.7745252321931338.22547476781
6413851875.90342972404-490.903429724039
6510471352.21802626344-305.218026263436
6610071007.57440237206-0.57440237205833
67842967.561899462682-125.561899462682
68827799.82881699920827.1711830007924
69711785.420247075442-74.4202470754418
70443667.800355427739-224.800355427739
71313394.907167989259-81.9071679892587
72202263.124309929431-61.1243099294309
73473150.793828467498322.206171532502
74566428.80723015071137.19276984929
751609524.7934796021381084.20652039786
7612961591.39320085807-295.393200858068
7711531271.96343211015-118.963432110146
7811551126.3739772557228.6260227442831
798591128.9970745575-269.997074557496
80798827.120098557448-29.120098557448
81557765.486246799529-208.486246799529
82402519.948165522949-117.948165522949
83223362.380809787098-139.380809787098
84153180.34693367815-27.3469336781497
85548109.751678069678438.248321930322
86647514.290947612753132.709052387247
871757616.1796008218561140.82039917814
8813261751.01162582555-425.011625825546
8913081310.76047697954-2.76047697953868
9011751292.70039019162-117.70039019162
919921157.13842773523-165.138427735227
92808970.543890357086-162.543890357086
93758783.005827790488-25.0058277904875
94551732.461530597539-181.461530597539
95310521.511691281681-211.511691281681
96146275.907755718938-129.907755718938
97649109.08007781231539.91992218769
98602623.832414128714-21.8324141287138
991801576.3571920394821224.64280796052
10014811802.01376379238-321.013763792383
10114001475.02631702621-75.0263170262106
10213191392.39323316685-73.3932331668477
10311531309.79569633948-156.795696339479
1049501140.38275364072-190.382753640718
105829933.23872772561-104.23872772561
106636809.96978276714-173.96978276714
107310613.18301493-303.18301493
108191280.583686751034-89.583686751034
109679159.633735338062519.366264661938
110842658.938684021877183.061315978123
1111975825.9233455679471149.07665443205
11216771983.93508294095-306.935082940955
11314181679.2540841969-261.254084196902
11415401414.56741523852125.432584761479
11511731539.297682933-366.297682932996
1169411164.32454953887-223.324549538872
117989927.46348569211561.5365143078848
118614976.802939529927-362.802939529927
119352593.905875564109-241.905875564109
120405326.64035545693578.3596445430652

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2698 & 710 & 1988 \tabularnewline
4 & 2367 & 2582.2724254781 & -215.272425478103 \tabularnewline
5 & 1928 & 2246.58663071503 & -318.586630715029 \tabularnewline
6 & 1846 & 1800.65201490218 & 45.347985097816 \tabularnewline
7 & 1404 & 1719.63909604189 & -315.639096041886 \tabularnewline
8 & 1316 & 1270.76863866691 & 45.2313613330882 \tabularnewline
9 & 1008 & 1183.75318127886 & -175.753181278863 \tabularnewline
10 & 865 & 871.927594538708 & -6.92759453870758 \tabularnewline
11 & 586 & 728.776802879543 & -142.776802879543 \tabularnewline
12 & 343 & 446.669006821894 & -103.669006821894 \tabularnewline
13 & 1143 & 201.412462872151 & 941.587537127849 \tabularnewline
14 & 1807 & 1021.90782330046 & 785.092176699542 \tabularnewline
15 & 2380 & 1702.99677838581 & 677.003221614193 \tabularnewline
16 & 2334 & 2290.73298133135 & 43.2670186686519 \tabularnewline
17 & 2116 & 2245.67476646264 & -129.674766462635 \tabularnewline
18 & 1788 & 2024.85215998973 & -236.852159989726 \tabularnewline
19 & 1571 & 1691.69664316755 & -120.696643167551 \tabularnewline
20 & 1306 & 1472.06946183107 & -166.069461831069 \tabularnewline
21 & 952 & 1203.45465880729 & -251.45465880729 \tabularnewline
22 & 806 & 843.981292114956 & -37.9812921149559 \tabularnewline
23 & 473 & 697.154560408413 & -224.154560408413 \tabularnewline
24 & 278 & 359.275429869756 & -81.2754298697564 \tabularnewline
25 & 993 & 162.506322735833 & 830.493677264167 \tabularnewline
26 & 1038 & 895.583523822075 & 142.416476177925 \tabularnewline
27 & 2259 & 943.683476715568 & 1315.31652328443 \tabularnewline
28 & 2283 & 2193.31372633023 & 89.6862736697726 \tabularnewline
29 & 1746 & 2219.26591073354 & -473.265910733539 \tabularnewline
30 & 1515 & 1671.96441986154 & -156.964419861536 \tabularnewline
31 & 1230 & 1437.54780458932 & -207.547804589316 \tabularnewline
32 & 882 & 1148.03015020942 & -266.030150209419 \tabularnewline
33 & 1028 & 794.239521512304 & 233.760478487696 \tabularnewline
34 & 704 & 945.327742279449 & -241.327742279449 \tabularnewline
35 & 390 & 616.074806291729 & -226.074806291729 \tabularnewline
36 & 238 & 297.153878118824 & -59.1538781188242 \tabularnewline
37 & 594 & 143.866286678866 & 450.133713321134 \tabularnewline
38 & 692 & 509.664263321155 & 182.335736678845 \tabularnewline
39 & 2125 & 611.63313131785 & 1513.36686868215 \tabularnewline
40 & 1849 & 2077.57430588831 & -228.574305888312 \tabularnewline
41 & 1468 & 1796.59897157354 & -328.598971573543 \tabularnewline
42 & 1531 & 1408.44641900332 & 122.553580996677 \tabularnewline
43 & 1203 & 1474.11401995944 & -271.114019959437 \tabularnewline
44 & 878 & 1140.212731617 & -262.212731617 \tabularnewline
45 & 818 & 809.505195958898 & 8.49480404110193 \tabularnewline
46 & 605 & 749.690100775206 & -144.690100775206 \tabularnewline
47 & 316 & 533.540658318861 & -217.540658318861 \tabularnewline
48 & 136 & 239.805491354293 & -103.805491354293 \tabularnewline
49 & 528 & 57.5459765711709 & 470.454023428829 \tabularnewline
50 & 654 & 459.786261616291 & 194.213738383709 \tabularnewline
51 & 1892 & 590.013675862283 & 1301.98632413772 \tabularnewline
52 & 1597 & 1856.35376951659 & -259.353769516588 \tabularnewline
53 & 1515 & 1555.70846435368 & -40.708464353675 \tabularnewline
54 & 1241 & 1472.8223707973 & -231.8223707973 \tabularnewline
55 & 1026 & 1193.77633645903 & -167.776336459029 \tabularnewline
56 & 758 & 975.124380213349 & -217.124380213349 \tabularnewline
57 & 733 & 702.398274296718 & 30.6017257032817 \tabularnewline
58 & 481 & 678.064376356576 & -197.064376356576 \tabularnewline
59 & 280 & 421.774912805128 & -141.774912805128 \tabularnewline
60 & 117 & 217.688924701997 & -100.688924701997 \tabularnewline
61 & 651 & 52.4972476443319 & 598.502752355668 \tabularnewline
62 & 611 & 599.524745506379 & 11.4752544936206 \tabularnewline
63 & 1898 & 559.774525232193 & 1338.22547476781 \tabularnewline
64 & 1385 & 1875.90342972404 & -490.903429724039 \tabularnewline
65 & 1047 & 1352.21802626344 & -305.218026263436 \tabularnewline
66 & 1007 & 1007.57440237206 & -0.57440237205833 \tabularnewline
67 & 842 & 967.561899462682 & -125.561899462682 \tabularnewline
68 & 827 & 799.828816999208 & 27.1711830007924 \tabularnewline
69 & 711 & 785.420247075442 & -74.4202470754418 \tabularnewline
70 & 443 & 667.800355427739 & -224.800355427739 \tabularnewline
71 & 313 & 394.907167989259 & -81.9071679892587 \tabularnewline
72 & 202 & 263.124309929431 & -61.1243099294309 \tabularnewline
73 & 473 & 150.793828467498 & 322.206171532502 \tabularnewline
74 & 566 & 428.80723015071 & 137.19276984929 \tabularnewline
75 & 1609 & 524.793479602138 & 1084.20652039786 \tabularnewline
76 & 1296 & 1591.39320085807 & -295.393200858068 \tabularnewline
77 & 1153 & 1271.96343211015 & -118.963432110146 \tabularnewline
78 & 1155 & 1126.37397725572 & 28.6260227442831 \tabularnewline
79 & 859 & 1128.9970745575 & -269.997074557496 \tabularnewline
80 & 798 & 827.120098557448 & -29.120098557448 \tabularnewline
81 & 557 & 765.486246799529 & -208.486246799529 \tabularnewline
82 & 402 & 519.948165522949 & -117.948165522949 \tabularnewline
83 & 223 & 362.380809787098 & -139.380809787098 \tabularnewline
84 & 153 & 180.34693367815 & -27.3469336781497 \tabularnewline
85 & 548 & 109.751678069678 & 438.248321930322 \tabularnewline
86 & 647 & 514.290947612753 & 132.709052387247 \tabularnewline
87 & 1757 & 616.179600821856 & 1140.82039917814 \tabularnewline
88 & 1326 & 1751.01162582555 & -425.011625825546 \tabularnewline
89 & 1308 & 1310.76047697954 & -2.76047697953868 \tabularnewline
90 & 1175 & 1292.70039019162 & -117.70039019162 \tabularnewline
91 & 992 & 1157.13842773523 & -165.138427735227 \tabularnewline
92 & 808 & 970.543890357086 & -162.543890357086 \tabularnewline
93 & 758 & 783.005827790488 & -25.0058277904875 \tabularnewline
94 & 551 & 732.461530597539 & -181.461530597539 \tabularnewline
95 & 310 & 521.511691281681 & -211.511691281681 \tabularnewline
96 & 146 & 275.907755718938 & -129.907755718938 \tabularnewline
97 & 649 & 109.08007781231 & 539.91992218769 \tabularnewline
98 & 602 & 623.832414128714 & -21.8324141287138 \tabularnewline
99 & 1801 & 576.357192039482 & 1224.64280796052 \tabularnewline
100 & 1481 & 1802.01376379238 & -321.013763792383 \tabularnewline
101 & 1400 & 1475.02631702621 & -75.0263170262106 \tabularnewline
102 & 1319 & 1392.39323316685 & -73.3932331668477 \tabularnewline
103 & 1153 & 1309.79569633948 & -156.795696339479 \tabularnewline
104 & 950 & 1140.38275364072 & -190.382753640718 \tabularnewline
105 & 829 & 933.23872772561 & -104.23872772561 \tabularnewline
106 & 636 & 809.96978276714 & -173.96978276714 \tabularnewline
107 & 310 & 613.18301493 & -303.18301493 \tabularnewline
108 & 191 & 280.583686751034 & -89.583686751034 \tabularnewline
109 & 679 & 159.633735338062 & 519.366264661938 \tabularnewline
110 & 842 & 658.938684021877 & 183.061315978123 \tabularnewline
111 & 1975 & 825.923345567947 & 1149.07665443205 \tabularnewline
112 & 1677 & 1983.93508294095 & -306.935082940955 \tabularnewline
113 & 1418 & 1679.2540841969 & -261.254084196902 \tabularnewline
114 & 1540 & 1414.56741523852 & 125.432584761479 \tabularnewline
115 & 1173 & 1539.297682933 & -366.297682932996 \tabularnewline
116 & 941 & 1164.32454953887 & -223.324549538872 \tabularnewline
117 & 989 & 927.463485692115 & 61.5365143078848 \tabularnewline
118 & 614 & 976.802939529927 & -362.802939529927 \tabularnewline
119 & 352 & 593.905875564109 & -241.905875564109 \tabularnewline
120 & 405 & 326.640355456935 & 78.3596445430652 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308251&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]2698[/C][C]710[/C][C]1988[/C][/ROW]
[ROW][C]4[/C][C]2367[/C][C]2582.2724254781[/C][C]-215.272425478103[/C][/ROW]
[ROW][C]5[/C][C]1928[/C][C]2246.58663071503[/C][C]-318.586630715029[/C][/ROW]
[ROW][C]6[/C][C]1846[/C][C]1800.65201490218[/C][C]45.347985097816[/C][/ROW]
[ROW][C]7[/C][C]1404[/C][C]1719.63909604189[/C][C]-315.639096041886[/C][/ROW]
[ROW][C]8[/C][C]1316[/C][C]1270.76863866691[/C][C]45.2313613330882[/C][/ROW]
[ROW][C]9[/C][C]1008[/C][C]1183.75318127886[/C][C]-175.753181278863[/C][/ROW]
[ROW][C]10[/C][C]865[/C][C]871.927594538708[/C][C]-6.92759453870758[/C][/ROW]
[ROW][C]11[/C][C]586[/C][C]728.776802879543[/C][C]-142.776802879543[/C][/ROW]
[ROW][C]12[/C][C]343[/C][C]446.669006821894[/C][C]-103.669006821894[/C][/ROW]
[ROW][C]13[/C][C]1143[/C][C]201.412462872151[/C][C]941.587537127849[/C][/ROW]
[ROW][C]14[/C][C]1807[/C][C]1021.90782330046[/C][C]785.092176699542[/C][/ROW]
[ROW][C]15[/C][C]2380[/C][C]1702.99677838581[/C][C]677.003221614193[/C][/ROW]
[ROW][C]16[/C][C]2334[/C][C]2290.73298133135[/C][C]43.2670186686519[/C][/ROW]
[ROW][C]17[/C][C]2116[/C][C]2245.67476646264[/C][C]-129.674766462635[/C][/ROW]
[ROW][C]18[/C][C]1788[/C][C]2024.85215998973[/C][C]-236.852159989726[/C][/ROW]
[ROW][C]19[/C][C]1571[/C][C]1691.69664316755[/C][C]-120.696643167551[/C][/ROW]
[ROW][C]20[/C][C]1306[/C][C]1472.06946183107[/C][C]-166.069461831069[/C][/ROW]
[ROW][C]21[/C][C]952[/C][C]1203.45465880729[/C][C]-251.45465880729[/C][/ROW]
[ROW][C]22[/C][C]806[/C][C]843.981292114956[/C][C]-37.9812921149559[/C][/ROW]
[ROW][C]23[/C][C]473[/C][C]697.154560408413[/C][C]-224.154560408413[/C][/ROW]
[ROW][C]24[/C][C]278[/C][C]359.275429869756[/C][C]-81.2754298697564[/C][/ROW]
[ROW][C]25[/C][C]993[/C][C]162.506322735833[/C][C]830.493677264167[/C][/ROW]
[ROW][C]26[/C][C]1038[/C][C]895.583523822075[/C][C]142.416476177925[/C][/ROW]
[ROW][C]27[/C][C]2259[/C][C]943.683476715568[/C][C]1315.31652328443[/C][/ROW]
[ROW][C]28[/C][C]2283[/C][C]2193.31372633023[/C][C]89.6862736697726[/C][/ROW]
[ROW][C]29[/C][C]1746[/C][C]2219.26591073354[/C][C]-473.265910733539[/C][/ROW]
[ROW][C]30[/C][C]1515[/C][C]1671.96441986154[/C][C]-156.964419861536[/C][/ROW]
[ROW][C]31[/C][C]1230[/C][C]1437.54780458932[/C][C]-207.547804589316[/C][/ROW]
[ROW][C]32[/C][C]882[/C][C]1148.03015020942[/C][C]-266.030150209419[/C][/ROW]
[ROW][C]33[/C][C]1028[/C][C]794.239521512304[/C][C]233.760478487696[/C][/ROW]
[ROW][C]34[/C][C]704[/C][C]945.327742279449[/C][C]-241.327742279449[/C][/ROW]
[ROW][C]35[/C][C]390[/C][C]616.074806291729[/C][C]-226.074806291729[/C][/ROW]
[ROW][C]36[/C][C]238[/C][C]297.153878118824[/C][C]-59.1538781188242[/C][/ROW]
[ROW][C]37[/C][C]594[/C][C]143.866286678866[/C][C]450.133713321134[/C][/ROW]
[ROW][C]38[/C][C]692[/C][C]509.664263321155[/C][C]182.335736678845[/C][/ROW]
[ROW][C]39[/C][C]2125[/C][C]611.63313131785[/C][C]1513.36686868215[/C][/ROW]
[ROW][C]40[/C][C]1849[/C][C]2077.57430588831[/C][C]-228.574305888312[/C][/ROW]
[ROW][C]41[/C][C]1468[/C][C]1796.59897157354[/C][C]-328.598971573543[/C][/ROW]
[ROW][C]42[/C][C]1531[/C][C]1408.44641900332[/C][C]122.553580996677[/C][/ROW]
[ROW][C]43[/C][C]1203[/C][C]1474.11401995944[/C][C]-271.114019959437[/C][/ROW]
[ROW][C]44[/C][C]878[/C][C]1140.212731617[/C][C]-262.212731617[/C][/ROW]
[ROW][C]45[/C][C]818[/C][C]809.505195958898[/C][C]8.49480404110193[/C][/ROW]
[ROW][C]46[/C][C]605[/C][C]749.690100775206[/C][C]-144.690100775206[/C][/ROW]
[ROW][C]47[/C][C]316[/C][C]533.540658318861[/C][C]-217.540658318861[/C][/ROW]
[ROW][C]48[/C][C]136[/C][C]239.805491354293[/C][C]-103.805491354293[/C][/ROW]
[ROW][C]49[/C][C]528[/C][C]57.5459765711709[/C][C]470.454023428829[/C][/ROW]
[ROW][C]50[/C][C]654[/C][C]459.786261616291[/C][C]194.213738383709[/C][/ROW]
[ROW][C]51[/C][C]1892[/C][C]590.013675862283[/C][C]1301.98632413772[/C][/ROW]
[ROW][C]52[/C][C]1597[/C][C]1856.35376951659[/C][C]-259.353769516588[/C][/ROW]
[ROW][C]53[/C][C]1515[/C][C]1555.70846435368[/C][C]-40.708464353675[/C][/ROW]
[ROW][C]54[/C][C]1241[/C][C]1472.8223707973[/C][C]-231.8223707973[/C][/ROW]
[ROW][C]55[/C][C]1026[/C][C]1193.77633645903[/C][C]-167.776336459029[/C][/ROW]
[ROW][C]56[/C][C]758[/C][C]975.124380213349[/C][C]-217.124380213349[/C][/ROW]
[ROW][C]57[/C][C]733[/C][C]702.398274296718[/C][C]30.6017257032817[/C][/ROW]
[ROW][C]58[/C][C]481[/C][C]678.064376356576[/C][C]-197.064376356576[/C][/ROW]
[ROW][C]59[/C][C]280[/C][C]421.774912805128[/C][C]-141.774912805128[/C][/ROW]
[ROW][C]60[/C][C]117[/C][C]217.688924701997[/C][C]-100.688924701997[/C][/ROW]
[ROW][C]61[/C][C]651[/C][C]52.4972476443319[/C][C]598.502752355668[/C][/ROW]
[ROW][C]62[/C][C]611[/C][C]599.524745506379[/C][C]11.4752544936206[/C][/ROW]
[ROW][C]63[/C][C]1898[/C][C]559.774525232193[/C][C]1338.22547476781[/C][/ROW]
[ROW][C]64[/C][C]1385[/C][C]1875.90342972404[/C][C]-490.903429724039[/C][/ROW]
[ROW][C]65[/C][C]1047[/C][C]1352.21802626344[/C][C]-305.218026263436[/C][/ROW]
[ROW][C]66[/C][C]1007[/C][C]1007.57440237206[/C][C]-0.57440237205833[/C][/ROW]
[ROW][C]67[/C][C]842[/C][C]967.561899462682[/C][C]-125.561899462682[/C][/ROW]
[ROW][C]68[/C][C]827[/C][C]799.828816999208[/C][C]27.1711830007924[/C][/ROW]
[ROW][C]69[/C][C]711[/C][C]785.420247075442[/C][C]-74.4202470754418[/C][/ROW]
[ROW][C]70[/C][C]443[/C][C]667.800355427739[/C][C]-224.800355427739[/C][/ROW]
[ROW][C]71[/C][C]313[/C][C]394.907167989259[/C][C]-81.9071679892587[/C][/ROW]
[ROW][C]72[/C][C]202[/C][C]263.124309929431[/C][C]-61.1243099294309[/C][/ROW]
[ROW][C]73[/C][C]473[/C][C]150.793828467498[/C][C]322.206171532502[/C][/ROW]
[ROW][C]74[/C][C]566[/C][C]428.80723015071[/C][C]137.19276984929[/C][/ROW]
[ROW][C]75[/C][C]1609[/C][C]524.793479602138[/C][C]1084.20652039786[/C][/ROW]
[ROW][C]76[/C][C]1296[/C][C]1591.39320085807[/C][C]-295.393200858068[/C][/ROW]
[ROW][C]77[/C][C]1153[/C][C]1271.96343211015[/C][C]-118.963432110146[/C][/ROW]
[ROW][C]78[/C][C]1155[/C][C]1126.37397725572[/C][C]28.6260227442831[/C][/ROW]
[ROW][C]79[/C][C]859[/C][C]1128.9970745575[/C][C]-269.997074557496[/C][/ROW]
[ROW][C]80[/C][C]798[/C][C]827.120098557448[/C][C]-29.120098557448[/C][/ROW]
[ROW][C]81[/C][C]557[/C][C]765.486246799529[/C][C]-208.486246799529[/C][/ROW]
[ROW][C]82[/C][C]402[/C][C]519.948165522949[/C][C]-117.948165522949[/C][/ROW]
[ROW][C]83[/C][C]223[/C][C]362.380809787098[/C][C]-139.380809787098[/C][/ROW]
[ROW][C]84[/C][C]153[/C][C]180.34693367815[/C][C]-27.3469336781497[/C][/ROW]
[ROW][C]85[/C][C]548[/C][C]109.751678069678[/C][C]438.248321930322[/C][/ROW]
[ROW][C]86[/C][C]647[/C][C]514.290947612753[/C][C]132.709052387247[/C][/ROW]
[ROW][C]87[/C][C]1757[/C][C]616.179600821856[/C][C]1140.82039917814[/C][/ROW]
[ROW][C]88[/C][C]1326[/C][C]1751.01162582555[/C][C]-425.011625825546[/C][/ROW]
[ROW][C]89[/C][C]1308[/C][C]1310.76047697954[/C][C]-2.76047697953868[/C][/ROW]
[ROW][C]90[/C][C]1175[/C][C]1292.70039019162[/C][C]-117.70039019162[/C][/ROW]
[ROW][C]91[/C][C]992[/C][C]1157.13842773523[/C][C]-165.138427735227[/C][/ROW]
[ROW][C]92[/C][C]808[/C][C]970.543890357086[/C][C]-162.543890357086[/C][/ROW]
[ROW][C]93[/C][C]758[/C][C]783.005827790488[/C][C]-25.0058277904875[/C][/ROW]
[ROW][C]94[/C][C]551[/C][C]732.461530597539[/C][C]-181.461530597539[/C][/ROW]
[ROW][C]95[/C][C]310[/C][C]521.511691281681[/C][C]-211.511691281681[/C][/ROW]
[ROW][C]96[/C][C]146[/C][C]275.907755718938[/C][C]-129.907755718938[/C][/ROW]
[ROW][C]97[/C][C]649[/C][C]109.08007781231[/C][C]539.91992218769[/C][/ROW]
[ROW][C]98[/C][C]602[/C][C]623.832414128714[/C][C]-21.8324141287138[/C][/ROW]
[ROW][C]99[/C][C]1801[/C][C]576.357192039482[/C][C]1224.64280796052[/C][/ROW]
[ROW][C]100[/C][C]1481[/C][C]1802.01376379238[/C][C]-321.013763792383[/C][/ROW]
[ROW][C]101[/C][C]1400[/C][C]1475.02631702621[/C][C]-75.0263170262106[/C][/ROW]
[ROW][C]102[/C][C]1319[/C][C]1392.39323316685[/C][C]-73.3932331668477[/C][/ROW]
[ROW][C]103[/C][C]1153[/C][C]1309.79569633948[/C][C]-156.795696339479[/C][/ROW]
[ROW][C]104[/C][C]950[/C][C]1140.38275364072[/C][C]-190.382753640718[/C][/ROW]
[ROW][C]105[/C][C]829[/C][C]933.23872772561[/C][C]-104.23872772561[/C][/ROW]
[ROW][C]106[/C][C]636[/C][C]809.96978276714[/C][C]-173.96978276714[/C][/ROW]
[ROW][C]107[/C][C]310[/C][C]613.18301493[/C][C]-303.18301493[/C][/ROW]
[ROW][C]108[/C][C]191[/C][C]280.583686751034[/C][C]-89.583686751034[/C][/ROW]
[ROW][C]109[/C][C]679[/C][C]159.633735338062[/C][C]519.366264661938[/C][/ROW]
[ROW][C]110[/C][C]842[/C][C]658.938684021877[/C][C]183.061315978123[/C][/ROW]
[ROW][C]111[/C][C]1975[/C][C]825.923345567947[/C][C]1149.07665443205[/C][/ROW]
[ROW][C]112[/C][C]1677[/C][C]1983.93508294095[/C][C]-306.935082940955[/C][/ROW]
[ROW][C]113[/C][C]1418[/C][C]1679.2540841969[/C][C]-261.254084196902[/C][/ROW]
[ROW][C]114[/C][C]1540[/C][C]1414.56741523852[/C][C]125.432584761479[/C][/ROW]
[ROW][C]115[/C][C]1173[/C][C]1539.297682933[/C][C]-366.297682932996[/C][/ROW]
[ROW][C]116[/C][C]941[/C][C]1164.32454953887[/C][C]-223.324549538872[/C][/ROW]
[ROW][C]117[/C][C]989[/C][C]927.463485692115[/C][C]61.5365143078848[/C][/ROW]
[ROW][C]118[/C][C]614[/C][C]976.802939529927[/C][C]-362.802939529927[/C][/ROW]
[ROW][C]119[/C][C]352[/C][C]593.905875564109[/C][C]-241.905875564109[/C][/ROW]
[ROW][C]120[/C][C]405[/C][C]326.640355456935[/C][C]78.3596445430652[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308251&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308251&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326987101988
423672582.2724254781-215.272425478103
519282246.58663071503-318.586630715029
618461800.6520149021845.347985097816
714041719.63909604189-315.639096041886
813161270.7686386669145.2313613330882
910081183.75318127886-175.753181278863
10865871.927594538708-6.92759453870758
11586728.776802879543-142.776802879543
12343446.669006821894-103.669006821894
131143201.412462872151941.587537127849
1418071021.90782330046785.092176699542
1523801702.99677838581677.003221614193
1623342290.7329813313543.2670186686519
1721162245.67476646264-129.674766462635
1817882024.85215998973-236.852159989726
1915711691.69664316755-120.696643167551
2013061472.06946183107-166.069461831069
219521203.45465880729-251.45465880729
22806843.981292114956-37.9812921149559
23473697.154560408413-224.154560408413
24278359.275429869756-81.2754298697564
25993162.506322735833830.493677264167
261038895.583523822075142.416476177925
272259943.6834767155681315.31652328443
2822832193.3137263302389.6862736697726
2917462219.26591073354-473.265910733539
3015151671.96441986154-156.964419861536
3112301437.54780458932-207.547804589316
328821148.03015020942-266.030150209419
331028794.239521512304233.760478487696
34704945.327742279449-241.327742279449
35390616.074806291729-226.074806291729
36238297.153878118824-59.1538781188242
37594143.866286678866450.133713321134
38692509.664263321155182.335736678845
392125611.633131317851513.36686868215
4018492077.57430588831-228.574305888312
4114681796.59897157354-328.598971573543
4215311408.44641900332122.553580996677
4312031474.11401995944-271.114019959437
448781140.212731617-262.212731617
45818809.5051959588988.49480404110193
46605749.690100775206-144.690100775206
47316533.540658318861-217.540658318861
48136239.805491354293-103.805491354293
4952857.5459765711709470.454023428829
50654459.786261616291194.213738383709
511892590.0136758622831301.98632413772
5215971856.35376951659-259.353769516588
5315151555.70846435368-40.708464353675
5412411472.8223707973-231.8223707973
5510261193.77633645903-167.776336459029
56758975.124380213349-217.124380213349
57733702.39827429671830.6017257032817
58481678.064376356576-197.064376356576
59280421.774912805128-141.774912805128
60117217.688924701997-100.688924701997
6165152.4972476443319598.502752355668
62611599.52474550637911.4752544936206
631898559.7745252321931338.22547476781
6413851875.90342972404-490.903429724039
6510471352.21802626344-305.218026263436
6610071007.57440237206-0.57440237205833
67842967.561899462682-125.561899462682
68827799.82881699920827.1711830007924
69711785.420247075442-74.4202470754418
70443667.800355427739-224.800355427739
71313394.907167989259-81.9071679892587
72202263.124309929431-61.1243099294309
73473150.793828467498322.206171532502
74566428.80723015071137.19276984929
751609524.7934796021381084.20652039786
7612961591.39320085807-295.393200858068
7711531271.96343211015-118.963432110146
7811551126.3739772557228.6260227442831
798591128.9970745575-269.997074557496
80798827.120098557448-29.120098557448
81557765.486246799529-208.486246799529
82402519.948165522949-117.948165522949
83223362.380809787098-139.380809787098
84153180.34693367815-27.3469336781497
85548109.751678069678438.248321930322
86647514.290947612753132.709052387247
871757616.1796008218561140.82039917814
8813261751.01162582555-425.011625825546
8913081310.76047697954-2.76047697953868
9011751292.70039019162-117.70039019162
919921157.13842773523-165.138427735227
92808970.543890357086-162.543890357086
93758783.005827790488-25.0058277904875
94551732.461530597539-181.461530597539
95310521.511691281681-211.511691281681
96146275.907755718938-129.907755718938
97649109.08007781231539.91992218769
98602623.832414128714-21.8324141287138
991801576.3571920394821224.64280796052
10014811802.01376379238-321.013763792383
10114001475.02631702621-75.0263170262106
10213191392.39323316685-73.3932331668477
10311531309.79569633948-156.795696339479
1049501140.38275364072-190.382753640718
105829933.23872772561-104.23872772561
106636809.96978276714-173.96978276714
107310613.18301493-303.18301493
108191280.583686751034-89.583686751034
109679159.633735338062519.366264661938
110842658.938684021877183.061315978123
1111975825.9233455679471149.07665443205
11216771983.93508294095-306.935082940955
11314181679.2540841969-261.254084196902
11415401414.56741523852125.432584761479
11511731539.297682933-366.297682932996
1169411164.32454953887-223.324549538872
117989927.46348569211561.5365143078848
118614976.802939529927-362.802939529927
119352593.905875564109-241.905875564109
120405326.64035545693578.3596445430652







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121381.345995235094-516.0369070913761278.72889756156
122357.691990470188-925.2854646873831640.66944562776
123334.037985705282-1254.347458808081922.42343021865
124310.383980940376-1543.495915995672164.26387787642
125286.72997617547-1808.145030927692381.60498327863
126263.075971410564-2056.10993724042582.26188006153
127239.421966645658-2291.980749624642770.82468291595
128215.767961880752-2518.71438103712950.2503047986
129192.113957115846-2738.341345977783122.56926020947
130168.45995235094-2952.323058404323289.2429631062
131144.805947586034-3161.749922692653451.36181786472
132121.151942821128-3367.459061830263609.76294747252

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 381.345995235094 & -516.036907091376 & 1278.72889756156 \tabularnewline
122 & 357.691990470188 & -925.285464687383 & 1640.66944562776 \tabularnewline
123 & 334.037985705282 & -1254.34745880808 & 1922.42343021865 \tabularnewline
124 & 310.383980940376 & -1543.49591599567 & 2164.26387787642 \tabularnewline
125 & 286.72997617547 & -1808.14503092769 & 2381.60498327863 \tabularnewline
126 & 263.075971410564 & -2056.1099372404 & 2582.26188006153 \tabularnewline
127 & 239.421966645658 & -2291.98074962464 & 2770.82468291595 \tabularnewline
128 & 215.767961880752 & -2518.7143810371 & 2950.2503047986 \tabularnewline
129 & 192.113957115846 & -2738.34134597778 & 3122.56926020947 \tabularnewline
130 & 168.45995235094 & -2952.32305840432 & 3289.2429631062 \tabularnewline
131 & 144.805947586034 & -3161.74992269265 & 3451.36181786472 \tabularnewline
132 & 121.151942821128 & -3367.45906183026 & 3609.76294747252 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308251&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]381.345995235094[/C][C]-516.036907091376[/C][C]1278.72889756156[/C][/ROW]
[ROW][C]122[/C][C]357.691990470188[/C][C]-925.285464687383[/C][C]1640.66944562776[/C][/ROW]
[ROW][C]123[/C][C]334.037985705282[/C][C]-1254.34745880808[/C][C]1922.42343021865[/C][/ROW]
[ROW][C]124[/C][C]310.383980940376[/C][C]-1543.49591599567[/C][C]2164.26387787642[/C][/ROW]
[ROW][C]125[/C][C]286.72997617547[/C][C]-1808.14503092769[/C][C]2381.60498327863[/C][/ROW]
[ROW][C]126[/C][C]263.075971410564[/C][C]-2056.1099372404[/C][C]2582.26188006153[/C][/ROW]
[ROW][C]127[/C][C]239.421966645658[/C][C]-2291.98074962464[/C][C]2770.82468291595[/C][/ROW]
[ROW][C]128[/C][C]215.767961880752[/C][C]-2518.7143810371[/C][C]2950.2503047986[/C][/ROW]
[ROW][C]129[/C][C]192.113957115846[/C][C]-2738.34134597778[/C][C]3122.56926020947[/C][/ROW]
[ROW][C]130[/C][C]168.45995235094[/C][C]-2952.32305840432[/C][C]3289.2429631062[/C][/ROW]
[ROW][C]131[/C][C]144.805947586034[/C][C]-3161.74992269265[/C][C]3451.36181786472[/C][/ROW]
[ROW][C]132[/C][C]121.151942821128[/C][C]-3367.45906183026[/C][C]3609.76294747252[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308251&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308251&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121381.345995235094-516.0369070913761278.72889756156
122357.691990470188-925.2854646873831640.66944562776
123334.037985705282-1254.347458808081922.42343021865
124310.383980940376-1543.495915995672164.26387787642
125286.72997617547-1808.145030927692381.60498327863
126263.075971410564-2056.10993724042582.26188006153
127239.421966645658-2291.980749624642770.82468291595
128215.767961880752-2518.71438103712950.2503047986
129192.113957115846-2738.341345977783122.56926020947
130168.45995235094-2952.323058404323289.2429631062
131144.805947586034-3161.749922692653451.36181786472
132121.151942821128-3367.459061830263609.76294747252



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'multiplicative'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')